We are currently dealing with (n,m,d)-codes (sphere covering bound, sphere packing bound etc.) and one question to solve is:
We are now looking for a sphere packing of $\{0,1\}^6$ with radius $r$. What is the maximum of $r$, so that the spheres are disjoint?
I thought, a sphere packing is a maximal set $M$ of spheres such that all spheres are pairwise disjoint. (Wikipedia only says that it's an arrangement of pairwise disjoint spheres.)
If so, I could just use one sphere with radius $r=6$ and have the entire $\{0,1\}^6$ covered. Or is the goal to also maximize the size of $M$? Then with $r=2$, I could fit three pairwise disjoint spheres in $M$. That is the maximum for all radii.